Modelling method for forming a model simulating multilithologic filling of a sedimentary basin

ABSTRACT

A method for forming a 2D or 3D diffusive type model allowing simulation of multilithologic filling of a sedimentary basin over geologic periods.  
     The model is based on the numerical simulation of the evolution of a sedimentary basin, from the past to the present, in a series of time intervals. In each time interval, three major phenomena interact and are numerically modelled: basin deformation, sediment supply and transportation of these sediments in the deformed basin. To model sediment transportation, long-term permanent transportation (creeping, slow diffusion process, etc.), short-term transportation (due to rain and flood) and catastrophic transportation (notably due to cliff collapse) are taken into account using an exponential water velocity model.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention is a method for forming a model simulatingsedimentary filling of basins over large time and space scales.

[0003] The method according to the invention more particularly relatesto the formation of a numerical stratigraphic model allowing two orthree-dimensional (2D or 3D) simulation of the multilithologic fillingof a basin in order to simulate the stratigraphic response of thesedimentary system to variations in time of the eustasy, the subsidence,the sediment supply and the physical parameters governing sedimenttransportation in the basin.

[0004] 2. Description of the Prior Art

[0005] The advances recently made in geology, which gave birth duringthe last twenty years to seismic stratigraphy, then to geneticstratigraphy, have deeply modified the understanding of the history ofsedimentary filling of basins over substantial time and space by showingthe crucial influence of three main parameters : eustasy, tectonics andsedimentary flow.

[0006] Many models and notably deterministic numerical models have beenformed in order to apprehend the geometric and lithologic implicationsof these new approaches.

[0007] These numerical models simulate the transportation and thesedimentation (or the erosion) of sediments in the basin and are basedon a description of the nature, from an estimation of the eustasy, thesubsidence and the sediment supply. Eustasy is the variation of thesurface of the oceans simultaneously observed on all of the earth'ssurface, and subsidence is the absolute displacement in time of thebottom of a sedimentary basin in relation to a fixed reference level.These models thus allow testing the influence of various concepts(relationship between climate and eustasy, etc.) on the layout of thesedimentary units. Furthermore, applied to real cases, these modelsallow testing the coherence of the parameters introduced in the model,such as the eustatic and tectonic variations, and to reinforce thegeologic interpretation of the studied basin.

[0008] A model is expected to define the main facies variationtendencies (variation of the sand/clay ratio, carbonate content, etc.)within the genetic units. It is therefore necessary to design amultilithologic modelling. The model must be able to simulate thetransportation and the sedimentation of various siliciclastic (sand,clay, etc.) and carbonate (reef, carbonate deep-sea ooze, bioclasts,etc.) lithologies so that these facies variation tendencies are a resultof the model, independent of geologic a priorisms such as sandy alluvialplain and clayey marine domain. In this ideal model, the siliciclasticsediments are carried along by rivers and ocean currents into the basin,whereas the carbonates are produced in marine domains, taking intoaccount the bathymetry, the turbidity of the water and the action of thewaves. After being carried along to the basin boundaries or produced inthe basin, the sediments are transported, then sedimented.

[0009] There are three main deterministic model families which governsediment transportation:

[0010] the particulate models based on the solution of the movement ofparticles (calculation of the flow of water, then relation between waterflow and sediment flow),

[0011] the diffusive models based on a diffusion equation where thedefinition of the diffusion coefficient is refined (taking account ofseveral lithologies, of the water flow, of the deposit environment,etc.), and

[0012] the geometric models based on a definition of the geometricprofile of the deposit environments (length and slope of the alluvialplain, etc.) or on a geometric definition of the sedimentation rate(exponential decrease in marine domains, etc.).

[0013] The particulate models use a careful description of thesedimentary processes and are therefore as chaotic as nature. Theyessentially allow obtaining simulations on reservoir scale (length ofthe order of 0.5 to 50 km and duration of the order of 5 to 500 ka). Thediffusive and geometric models both provide rough approximations ofnatural processes. They are much more stable than the reality theyaccount for, but they provide only a smoothed estimation of nature.These models are preferably applicable on basin scale (length of theorder of 10 to 1000 km and duration of the order of 0.1 to 100 Ma). Thegeometric models, based on an approximation of the basin setting, areessentially applicable in simple 2D cases wherein the subsidence, thenature of the sediments and the climate do not disturb the definition ofthe equilibrium profile too much. More general, the diffusive models,based on an approximation of the physics of the sediments, areapplicable in 3D and can deal with transportation and sedimentation ofmultiple lithologies.

[0014] Various known diffusive models are for example described by:

[0015] Kenyon and Turcotte, 1985, Morphology of a Delta Prograding byBulk Sediment Transport. In Geol. Soc. Amer. Bull., 96, 1457-1465,

[0016] Begin, Z. B., 1988, Application of a Diffusion-Erosion Model toAlluvial Channels which Degrad Due to Base-Level Lowering. Earth SurfaceProcesses and Landforms, 13, 487-500,

[0017] Rivenaes, J. C., 1988, Application of a Dual-LithologyDepth-Dependent Diffusion Equation in Stratigraphic Simulation. BasinResearch, 4, 133-146.

[0018] One advantage of diffusive models is that they allow returning togeologic concepts by quantifying certain relations such as the variableduration of the progradation and retrogradation stages of the geneticunits, or the evolution of the sandiness as a function of either thebathymetry, or the prograding or retrograding tendency of the longshore.

[0019] The goal of the prior models is essentially a numericalapproximation of theoretical concepts along profiles in 2D.

[0020] French patent 2,744,224 filed by the assignee describes a methodfor simulating the filling of a sedimentary basin. From known data onthe architecture of a basin and from measured data : well logs, seismicsurveys, etc., a set of input data is formed, which relates to theaccommodation created by subsidence and eustasy, to the supply andproduction of fluvial or marine sediments, and to physicaltransportation parameters such as diffusion coefficients of the variouslithologies. This data set is applied to a numerical model. The results,that can be deduced on the geometry and the lithologies of thesedimentary units, are compared with the measured data and the inputdata are refined step by step by inversion.

SUMMARY OF THE INVENTION

[0021] The modelling method according to the invention allows forming adiffusive type deterministic model (in 2D or 3D) simulating themultilithologic filling of a sedimentary basin. It comprises, from knownfield data relative to the architecture of the basin and from measureddata such as well log data or seismic data, forming a set of input datarelative to an accommodation available through subsidence and eustasy,to the supply of fluvial or marine sediments and the transportationthereof, and to physical parameters such as diffusion coefficients ofthe various lithologies, by means of an iterative process involvinggridding of the basin into grid cells of regular dimensions; modellingaccording to an explicit finite-volume scheme with constant timeintervals, so as to simulate the flow of each lithology deposited oneach grid cell; comparing the simulation results with the field data andmodifying the input data step by step and by inversion.

[0022] The method of the invention relates to the formation of anumerical deterministic diffusive type model allowing 2D or 3Dsimulation of the filling of sedimentary basins by siliclastic andcarbonate sediments.

[0023] The method comprises, in each time interval and for eachlithology:

[0024] modelling by deterministic equations respectively:

[0025] (1) the mean of the transportation processes acting on apermanent and continuous basis in the long term (more than a few years),

[0026] (2) the mean of the transportation processes acting on apermanent and continuous basis in the short term (of the order of a fewdays to a few months),

[0027] (3) the mean of the transportation processes acting in acatastrophic way in the very short term (of the order of a few hours toa few days), and

[0028] determining the resulting stratigraphy of the basin by takingaccount of the mass conservation.

[0029] The method comprises for example:

[0030] modelling long-term flows of sediments carried along by water byaccounting for a model of distribution of the water flows in the basinand of the sediment transportation capacity of such flows;

[0031] modelling short-term flows of sediments carried along by waterusing an exponential model for estimating the water velocity; and

[0032] modelling catastrophic flows carried along by water in unstablezones located by applying a critical slope criterion.

[0033] The diffusive model obtained by means of the method allowsapprehending in 3D the mulilithologic filling of a basin. In order toapply it to an industrial context, a parameter inversion methodology isused. Analysis of the available data, such as well or seismic data,allows estimation of a first set of parameters (eustasy, subsidence,sediment supply, etc.) required by the model. The diffusive model isthen used to obtain a first basin simulation. This simulation iscompared with the data. The parameters are then modified in order toreduce the differences between data and simulation. This inversion loop(simulation—comparison—modification) is continued and allows progressiverefinement of the quantification of each parameter. At the end of thisinversion loop, the user of the model thus has a simulation calibratedon the available data, as well as a set of physical parameters improvinghis knowledge of the basin studied.

[0034] Since modelling is carried out in a detailed way depending on thetransportation types, a more precise distribution of the sedimentswithin each geometry and a finer quantification of each one areobtained.

[0035] The main applications of the diffusive model and of its inversionloop according to the invention are:

[0036] quantification of the physical and geologic parameters (eustasy,subsidence, sediment source location, transportation parameters, etc.)for various geologic models, which allows to:

[0037] testing the coherence of various geologic models;

[0038] determining the best correlation scheme between different wells;

[0039] determining the best seismic data interpretation,

[0040] reconstituting the evolution in time of the stratigraphy of asedimentary basin, which allows in particular:

[0041] estimating the extension and the connectivity of the varioussedimentary units, or

[0042] estimating the regional distribution of the sedimentary facies.

[0043] In exploration, the model thus formed allows identifying thepotentially interesting regions through location and characterization ofthe sedimentary layers containing the mother rocks, the drain holes, thereservoirs and/or the overlying beds. Furthermore, reservoir engineerscan determine, from the model, the petrophysical properties of areservoir studied (mean porosity and permeability) and select the mostprospective production zones.

BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Other features and advantages of the method according to theinvention will be clear from reading the description hereafter of a nonlimitative embodiment example, with reference to the accompanyingdrawings wherein:

[0045]FIG. 1 is a flowchart of the method allowing modelling bysuccessive iterations the stratigraphy of a basin;

[0046]FIG. 2 illustrates the long-term (permanent) transportation modeof the sediments induced by rivers, ocean currents, or the slow actionof gravity (creeping, etc.); it is simulated by means of a diffusivemodel constrained by the water flow and a reduced availability; inmarine domains, the fine fraction of the sediments (clayey component) isfirst carried along by suspension, then reworked by the long-termprocesses acting on the sea bottom;

[0047]FIG. 3 illustrates the short-term transportation mode of sedimentsduring occasional but intense phenomena such as heavy rain inducingriver floods and hyperpycnal currents in marine domains; these processesare modelled by means of a diffusive model constrained by the waterflow, the reduced availability and the water velocity; this watervelocity is calculated by means of an exponential model; and

[0048]FIG. 4 illustrates the mass or catastrophic transportation mode ofsediments after cliff or slope collapse; the unstable zones are firstdetermined by means of a criterion on the slope of the soil; anysediment located above a critical slope is considered to be unstable; itis removed from the soil and displaced by means of Newton's equation(Acceleration=Gravity−Friction), as long as its velocity is above acritical velocity.

DETAILED DESCRIPTION OF THE INVENTION

[0049] The modelling method according to the invention allows obtaininga deterministic stratigraphic simulation over great lengths of time (ofthe order of ten thousand to millions of years) and over large distances(several tens to hundreds of kilometers), in 3D.

[0050] The sediments present in the basin studied can be defined bymeans of base lithologies. A lithology corresponds to a size grade andto a nature of grains. Coarse-grained sand, fine clays, mediumcarbonates can thus be distinguished for example.

[0051] As shown by the flowchart in FIG. 1, stratigraphic modelling ofthe basin is obtained iteratively from the past to the present (or atleast to a more recent time) in a series of constant time intervals, ofthe order of ten to one hundred thousand years. During each timeinterval, the stratigraphic model calculates the basin deformation andthe supply of each lithology, then it quantifies the transportation ofeach lithology. Application of the mass conservation allows obtaining anew geography and thus ends the time interval.

[0052] During a first stage, the accommodation available for thesediments is defined. The sediments are then introduced and sedimentaryproduction in the basin is simulated. These sediments are thereafterdistributed in accordance with macrotransportation laws which aredefined in the description hereafter by limiting erosion to theweathered layer.

[0053] I Accommodation Creation

[0054] The accommodation for sedimentary filling of the basin is the sumof the eustasy and of the subsidence. Sedimentary filling defines thebasin point by point, either from eustatic curves and subsidence maps,or directly from accommodation maps, therefore without using physicalmodels relating the eustasy to the climate, or the subsidence totectonic, isostatic or thermal processes.

[0055] Although it does not modify the accomodation, compactioninfluences the sedimentary filling by modifying the thickness of thesedimentary layers. In order to account for mechanical compaction, wehave chosen to directly relate the porosity of the sediments to themaximum depth of burial reached by them, by a relation of exponentialform allowing to obtain a good approximation of the compaction asdefined by:

[0056] Parasnis, D. S., 1960, The Compaction of Sediments and itsBearing on Some Geophysical Problems. Journal of the Royal AstronomicalSociety, Vol.3, No.1, pp; 1-28.

[0057] In order to account for the case of multilithologic sediments,the porosity of each lithology is considered independent of the others,which amounts to likening the sedimentary layers consisting of a mixtureof several lithologies such as sand and clay to a superposition ofmultiple sublayers consisting of pure lithologies. The porosity relatedto each lithology is thus dealt with individually according to themaximum depth of burial reached by the sedimentary layer.for  each  litho  log   y  i ⇒ Φ_(i) = Φ_(r, i) + (Φ_(o, i) − Φ_(r, i))^(−z/z_(i))${with}\quad \left\{ \begin{matrix}\Phi_{i} & {{porosity}\quad {of}\quad {litho}\quad \log \quad y\quad i\quad \left( {{in}\quad \%} \right)} \\\Phi_{r,i} & {{residual}\quad {porosity}\quad {of}\quad {litho}\quad \log \quad y\quad i\quad \left( {{in}\quad \%} \right)} \\\Phi_{o,i} & {{deposition}\quad {porosity}\quad {of}\quad {litho}\quad \log \quad y\quad i\quad \left( {{in}\quad \%} \right)} \\z & \text{maximum~~depth~~of~~burial~~reached~~by~~the~~sedimentary~~layer~~studied~~(in~~m)} \\z_{i} & {\text{reference~~depth~~of~~burial~~of}\quad {litho}\quad \log \quad y\quad i\quad \left( {{in}\quad m} \right)}\end{matrix} \right.$

[0058] This definition of porosity related to the lithologies allows inparticular to simulate the individual transportation of each lithologyand to deduce therefrom the consequences on the porosity of thesedimentary layers.

[0059] II Introduction and Production of Sediments

[0060] The accommodation being created, the second model formation stageconsists in introducing sediments in the basin or in producing them inthe marine domain.

[0061] a) Introduction of Sediments in the Domain Studied

[0062] The flows of sediments at the boundaries of the domain studiedgeologically represent the sediment supply responsible for filling ofthe basin. The flows can be physically perceived in terms of boundaryconditions of the sediment flow.

[0063] These boundary conditions are set either by imposing the exactvalue of the flow at one sector of the boundary, or by imposing acontinuous evolution on the sediment flow. The first case represents asupply zone imposed by conditions exterior to the basin, such as theoutlet of a river draining a river basin exterior to the basin. Thesecond case represents a free zone along which the sediment flow isgoverned by physical parameters interior to the basin, such as thecharacteristics of the waves. When simulating a basin, it is possible tocombine these two boundary condition types by distinguishing for examplea continental zone where the flow is imposed by the external riversupply and a marine zone where the flow is defined by the internaltransportation laws.

[0064] b) Sedimentary Production in the Domain Studied

[0065] The sediments can also be produced within the basin, moreparticularly in the case of carbonate sediments. For this stage ofconstruction of the model according to the invention, simulation of thisproduction is chosen by means of an empirical formula relating theproduction rate at each point of the basin to the bathymetry and to thesediment flows as defined for example by:

[0066] Lawrence et al., 1990, Stratigraphic Simulation of SedimentaryBasin: Concepts and Calibration in Amer. Assoc. Petrol. Geol. Bull., 74,3, 273-295.$\left. {\text{for~~each}\quad {litho}\quad \log \quad y\quad i}\Rightarrow P_{i} \right. = {P_{o,i}B_{i}{\prod\limits_{j \neq i}^{\quad}F_{j,i}}}$${with}\quad \left\{ {\begin{matrix}P_{i} & {\text{production~~rate~~of}\quad {litho}\quad \log \quad y\quad i\quad \left( {{in}\quad \text{m/s}} \right)} \\P_{o,i} & {\text{maximum~~production~~rate~~of}\quad {litho}\quad \log \quad y\quad i\quad \left( {{in}\quad \text{m/s}} \right)}\end{matrix}\left\{ \begin{matrix}{{\text{influence~~of~~bathymetry}\quad B_{i}} = \left\{ \begin{matrix}0 & {{{if}\quad b} \leq 0} \\\frac{b}{b_{i}} & {{{if}\quad 0} < b \leq {b_{i}\left\{ \begin{matrix}B_{i} & \text{influence~~of~~bathymetry~~(dimensionless)} \\b & \text{bathymetry~~(in~~m)} \\b_{i} & \text{bathymetric~~threshold~~(in~~m)} \\\beta_{i} & \left. {\text{attention~~coefficient~~(in}m^{- 1}} \right)\end{matrix} \right.}} \\^{- {\beta_{i}{({b - b_{i}})}}} & {{{if}\quad b} > b_{i}}\end{matrix} \right.} \\{{\text{influence~~of~~lithology}\quad j\quad F_{j,i}} = \left\{ {\begin{matrix}1 & {{{if}\quad Q_{j}} \leq S_{j,i}} \\^{- {\gamma_{j,i}{({Q_{j} - S_{j,i}})}}} & {{{if}\quad Q_{j}} > S_{j,i}}\end{matrix}\quad \left\{ \begin{matrix}F_{j,i} & {\text{sensitivity~~of}\quad {litho}\quad \log \quad y\quad i\quad \text{to~~the~~flow~~of}\quad {litho}\quad \log \quad y\quad j} \\Q_{j} & {\text{flow~~of}\quad {litho}\quad \log \quad y\quad j\quad \left( {{in}\quad m^{\overset{'}{e}}\text{/}s} \right)} \\S_{j,i} & {\text{initial~~inhibition~~threshold}\quad \left( {{in}\quad m^{\overset{'}{e}}\text{/}s} \right)} \\\gamma_{j,i} & {\text{sensitivity~~coefficient}\quad \left( {{in}\quad {m^{- 2} \cdot s}} \right)}\end{matrix} \right.} \right.}\end{matrix} \right.} \right.$

[0067] In order to account for the erosion of reefs when the reefsemerged, the process of mechanical alteration of the reefs has beensimulated considering that any reef sediment located in the weatheredlayer in the continental domain is changed into “bioclastic” sediment.The reef and bioclastic lithologies are transported in the basin likethe siliciclastic sediments.

[0068] III Sediment Transportation

[0069] a) Long-Term Transportation

[0070] Long-term processes correspond to the permanent transportation ofsediments, induced by rivers, ocean currents (FIG. 2) or the slow actionof gravity (creeping, etc.). Within the scope of the method, theseprocesses can be modelled by a diffusion equation constrained by thewater flow and by a reduced availability.

[0071] Defining the value of the water flow Qwater at each point M ofthe basin is the staring point. This calculation is carried out fromupstream to downstream, assuming that all of the water reaching a givenpoint of the basin is redistributed to neighboring point downstream fromthis point, proportionally to the slope; the neighboring point havingthe steepest slope thus receives more water than the others.

[0072] The long-term transportation capacity at any point M of the basinis then calculated. This transportation capacity is defined by adiffusive model constrained by the water flow,that is the transportationcapacity for each lithology is defined by the formula as follows:

{right arrow over (Q_(max,litho))}=−( K _(gravity) +K _(river) Q_(water)){right arrow over (grad)} z

[0073] with:

[0074] Qmax,litho the transportation capacity of the lithology “litho”at M,

[0075] Qwater the water stream flowing at the soil surface at M,

[0076] Kgravity the diffusion coefficient related to the permanentgravity processes (soil creeping, etc.),

[0077] Kriver the diffusion coefficient related to the permanent riverand ocean transportation,

[0078] z the altitude of the soil at M.

[0079] To define the real flow Qlitho of each lithology transported atpoint M, the basin is scanned from upstream to downstream. At each pointM of this path, the real flow of each lithology provided by the upstream(given that a previous calculation of what was happening upstream frompoint M) is known.

[0080] Furthermore consideration occurs that, locally, erosion cannotexceed a maximum value E defined by the lithology content in the soil (acarbonate reef thus erodes less quickly than a claystone, which erodesless quickly than a sandstone, etc.) and by the bathymetry (erosionbeing different in the open and in a submarine environment).

[0081] The real “outgoing” flow downstream from point M is calculatedconsidering that this flow cannot exceed the maximum transportationcapacity downstream from M, and cannot exceed the maximum sedimentavailability, defined as the sum of the “incoming” flow upstream and ofthe maximum erosion. Therefore:

Q _(litho)=min(Q _(litho upstream) +E _(litho) ; Q_(max,litho downstream)).

[0082] The assumption is that the flow remains diffusive, that isfollowing the greatest slope. A weighting coefficient λ ranging between0 and 1 is thus defined, such that:

{right arrow over (Q_(litho))}=λ{right arrow over (Q _(max,litho))}=−λ(K_(qravity) +K _(river) Q _(water)){right arrow over (grad)}z

[0083] b) Short-Term Transportation

[0084] Short-term processes correspond (FIG. 3) to the transportation ofsediments during occasional but intense phenomena such as heavy raininducing river floods and hyperpycnal currents in the marine domain.Within the scope of the invention, is consideration that the processescan be modelled by an improved diffusion equation constrained by thewater flow, by a reduced availability and by the velocity of flow of thewater.

[0085] Such an occasional sediment transportation has been the object ofmany studies for river, coastal and marine engineering problems. Thegoal of these studies is generally to determine the transportationcapacity of a water current in order to know if human installations suchas houses, bridges, ports or offshore platforms can withstand such acurrent. It is generally assumed that a stream can be characterized bythree main quantities: its velocity u, its depth h and its width w. Itis also generally assumed that the Saint-Venant equations correspondingto the formulation for a fluid of Newton's equation (sum of theforces=acceleration) allow determination of these characteristics at anypoint of a flow. The Saint-Venant equations are expressed in 2D in thesimplified form as follows: $\quad\left\{ \begin{matrix}\text{water~~volume~~conservation} & {\frac{h}{t} = {{\frac{\partial h}{\partial t} + \frac{\partial{uh}}{\partial x}} = 0}} \\\text{momentum~~and~~forces~~balance} & {\frac{{uh}}{t} = {{\frac{\partial{uh}}{\partial t} + \frac{{\partial u^{2}}h}{\partial x}} = {{ghS} - {Cu}^{2}}}}\end{matrix} \right.$

[0086] where S represents the slope of the soil surface and C thecoefficient of friction of the water against the soil.

[0087] Solution of these equations over very great lengths of time (tento several hundred thousand years) and over very large distances(several tens to hundreds of kilometers) poses considerable numericalproblems for practical application. The main problem is the calculatingtime required to solve these equations. It can come to several days fora single time interval. A stratigraphic simulation would therefore lastfor weeks.

[0088] To overcome this major obstacle, the method provided greatlysimplifies calculation of the velocity of the water.

[0089] First consideration is that an equilibrium regime existsvirtually. This equilibrium regime is defined by the uniform permanentsolution of the above equations. An equilibrium velocity Ue, anequilibrium height He and an equilibrium distance Le are defined by:$U_{e} = \left( \frac{Q_{water}{gS}}{C} \right)^{1/3}$$H_{e} = {\frac{Q_{water}}{U_{e}} = \left( \frac{{CQ}_{water}^{2}}{gS} \right)^{1/3}}$$L_{e} = {\frac{Q_{water}}{3U_{e}C} = \frac{H_{e}}{3C}}$

[0090] The velocity of a stream is connected to try at any point toreturn to an equilibrium velocity. This evolution tendency is assumed tofollow an exponential model:$\frac{\partial{U(M)}}{\partial\xi} = \frac{U_{e}}{L_{e}}$

[0091] where ξ is the distance along the flow.

[0092] In cases where the equilibrium velocity and distance remainsubstantially uniform between a reference point and point M, the aboverelation leads to the exponential model as follows:

U(M)=U _(e)+(U _(o) −U _(e))e ^(−ξ/L) ^(_(e))

[0093] where U_(o) represents the velocity at a reference point of theflow.

[0094] Furthermore consideration is given that the velocity of the wateracts as a weighting coefficient P(U) of the velocity model, according tothe relation as follows:$\overset{\rightarrow}{Q_{\max,{litho}}} = {{- \left( {K_{gravity} + {K_{river}Q_{water}{P(U)}}} \right)}\overset{\rightarrow}{grad}z\quad {with}}$${P(U)} = {{\left( \frac{U^{2} - U_{c,{litho}}^{2}}{U_{e}^{2}} \right)^{3/2}\quad {if}\quad U} > {U_{c,{litho}}\quad {and}}}$P(U) = 0  if  U < U_(c, litho)

[0095] where P(U) is the weighting coefficient depending on the velocityU of the flow, on the critical velocity Uc,litho from which thelithology “litho” can be transported and on the equilibrium velocity Ue.

[0096] Finally the availability rule given above concerning long-termtransportation to constrain and quantify the real flow of sedimentstransported by an occasional stream is applied.

[0097] c) Catastrophic Transportation

[0098] Catastrophic processes correspond to the mass transport ofsediments after cliff or slope collapse. The unstable zones are firstdetermined by applying a critical slope criterion. This critical slopevaries locally and depends on the lithologic nature of the sediments inthe soil.

[0099] Any unstable zone is then mass displaced by applying Newton'sequation: the collapse acceleration is equal to the sum of the forcesapplied (gravity and friction). This equation allows moving eachcollapse through the basin. The collapse is considered to be frozen assoon as its velocity decreases below a critical threshold.

[0100] d) Numerical Solution

[0101] Realization of the model according to the invention comprisesnumerical solution of the transportation equations based on spatialdiscretization of the basin studied and temporal discretization of theformation.

[0102] The basin studied is split up into square grid cells of constantsize, and filling of this grid pattern is simulated in a succession ofcalculating times separated by a constant time interval. The width ofthe grid cells is for example of the order of 1 to 10 kilometersdepending on the basin simulated, and the time interval is of the orderof 50,000 years.

[0103] The transportation equations are then solved by means of anexplicit numerical scheme where the physical parameters such as the flowor the altitude at the time (n+1) are expressed as a function ofparameters measured at the time (n) and whose values are thus known.

[0104] In the two-dimensional monolithologic case, this solution isexpressed as follows: $\begin{matrix}{Q = {\left. {{- K}\frac{\partial h}{\partial x}}\Rightarrow{{at}\quad {each}\quad {grid}\quad {cell}\quad i\quad Q_{i}^{({n + 1})}} \right. = {{- K_{i}^{(n)}}\frac{h_{i + 1}^{(n)} - h_{i}^{(n)}}{x}}}} & (1) \\{\begin{matrix}{\frac{\partial h}{\partial t} = \left. {- \frac{\partial Q}{\partial x}}\Rightarrow{{at}\quad {each}\quad {grid}\quad {cell}\quad i\quad \frac{h_{i + 1}^{({n + 1})} - h_{i}^{(n)}}{t}} \right.} \\{= {- \frac{Q_{i}^{({n + 1})} - Q_{i - 1}^{({n + 1})}}{x}}}\end{matrix}\quad} & (2) \\{{{i.e.\quad h_{i}^{({n + 1})}} = {h_{i}^{(n)} + {\frac{t}{x^{2}}\quad \left( {{K_{i}^{(n)}\frac{h_{i + 1}^{(n)} - h_{i}^{(n)}}{x}} - {K_{i}^{(n)}\frac{h_{i}^{(n)} - h_{i - 1}^{(n)}}{x}}} \right)}}}{{with}\quad \left\{ \begin{matrix}h_{i}^{(n)} & {{altitude}\quad {of}\quad {grid}\quad {cell}\quad i\quad {at}\quad {the}\quad {time}\quad n\quad \left( {{in}\quad m} \right)} \\K_{i}^{(n)} & {{diffusion}\quad {coefficient}\quad {at}\quad {grid}\quad {cell}\quad i\quad \left( {{in}\quad m^{2}\text{/s}} \right)} \\Q_{i}^{(n)} & {{{sediment}\quad {flow}\quad {between}\quad {grid}\quad {cells}\quad i\quad {and}\quad i} + {1\quad \left( {{in}\quad m^{2}\text{/s}} \right)}} \\{t} & {{time}\quad {interval}\quad \left( {{in}\quad s} \right)} \\{x} & {{grid}\quad {cell}\quad {width}\quad \left( {{in}\quad m} \right)}\end{matrix} \right.}} & \quad\end{matrix}$

[0105] This rather simple writing however becomes more complex whenswitching to multilithology and 3D and when taking account of therestriction of sediment transportation to the weathered layer. In thiscase, its writen:${\frac{\partial h}{\partial t} = {{- V_{i}}\quad \max}},{{i.e.h_{i}^{({n + 1})}} = {h_{i}^{(n)} - {V_{i} \cdot {t}}}}$

[0106] Explicit finite-volume solution is the fastest calculatingmethod. It furthermore provides very precise results within thestability range of the algorithm, which requires very small internalcalculation time intervals, of the order of one century to onemillennium.

[0107] Application of the model to the input data formed from the fielddata allows simulation of the transportation of sediments throughout thestudied basin. The simulation validity is then tested by comparing theresults provided by the model with the data collected in the field, andmainly the sediment thicknesses and the facies observed in the welllogs. In the case of a disagreement, the set of input parameters of themodel: accommodation and amount of sediments transported is sought byinversion such that the difference between the results obtained by theseparameters and the constraints applied is minimal, as schematizedhereafter. direct  model ⇒ S = M(p)deviation  function ⇒ E(p) = S − C${with}\left\{ {{\left. {\begin{matrix}p & \text{set~~of~~input~~parameters~~of~~the~~model} \\M & \text{set~~of~~equations~~governing~~the~~model} \\S & \text{set~~of~~results~~at~~the~~model~~output} \\C & \text{set~~of~~geologic~~constraints} \\E & \text{deviation~~function~~between~~results~~and~~constraints} \\{x} & \text{measurement~~of~~the~~deviation~~between~~results~~and~~constraints}\end{matrix}{inversion}}\Rightarrow{{find}\quad \overset{\sim}{p}\quad {such}\quad {that}\overset{\sim}{E}} \right. = {{E\left( \overset{\sim}{p} \right)}\quad {is}\quad {the}\quad {absolute}\quad {minimum}\quad {of}\quad {function}\quad E{\forall p}}},{{E(p)} \geq \overset{\sim}{E}}} \right.$

[0108] Within the context of the present invention, the goal ofinversion is thus to quantify in particular the values of accommodation,of the sediment supply and of the diffusion coefficients in order toobtain a simulation whose sedimentary body geometries, thicknesses andfacies measured at the level of the calibration wells are as close aspossible to the geologic constraints.

[0109] A trial-and-error type inversion method is used. An initial setof parameters is defined. The solution of the model related to theseparameters is calculated and the value of the parameters is modified asa function of the difference between the solution and the geologicconstraints. This procedure is continued until the difference becomessufficiently small.

[0110] The agreement optimum being reached, the simulation leads toquantitative data on the geometry of the basin and on the lithologies ofthe sedimentary units. It also allows checking the coherence of the wellcorrelation scheme.

[0111] IV Industrial Validation of the Model Obtained

[0112] The validity of the model thus formed has been tested on simpletwo or three-dimensional theoretical cases. The subsidence velocity, thesediment supply rate and the sediment diffusivity were for exampleassumed to be constant. By defining the eustasy according to one or twocyclicity orders, we have thus been able to show, by means of thesesimple but realistic cases, that the diffusive model allows restoringthe implications of the genetic stratigraphy concepts, such asvolumetric partitioning of the sediments in a genetic unit anddistortion of the genetic units. The geologic coherence of thesesimulation results allows empirically validating the use of themultilithologic diffusion equation over long time and space scales.

[0113] The model has also been tested on current and old real cases, invarious sedimentary contexts, within the scope of theses and projects incollaboration with oil companies. The tests were notably carried out on:

[0114] (1) siliciclastic systems (sand, clay, . . . ) in shallow deltaicto marine environments (bathymetry<200 m):

[0115] Mesa Verde formation, San Juan basin in Colorado, USA (basinlength=200 km, duration of the formation studied=10 Ma),

[0116] Brent formation, North Sea (basin surface area=250×350 km²,duration of the formation studied=12 Ma),

[0117] Tertiary and Quaternary formations, at the mouth of the Red Riverin Vietnam (basin surface area=120×90 km², duration of the formationstudied=30 Ma),

[0118] Secondary to Quaternary formations, Colorado basin, off Argentina(basin surface area=200×200 km², duration of the formation studied=240Ma),

[0119] (2) turbiditic siliciclastic systems (sand, clay, . . . ) inshallow to very deep marine environments (bathymetry up to 1000 m):

[0120] Pab formation, in Pakistan (basin surface area=90×110 km²,duration of the formation studied=3 Ma),

[0121] formation of Eocene age, along the Brazilian margin (basinsurface area=40×80 km², duration of the formation studied=15 Ma),

[0122] the formation of Eocene age of the Annot sandstone, in the Southof France (basin surface area=20×40 kM², duration of the formationstudied=15 Ma),

[0123] (3) pure carbonate systems (coral and rudistid reefs, deep-seaooze, . . . ) in shallow marine environments:

[0124] Natih formation, in Oman (basin surface area=200×200 km²,duration of the formation studied=10 Ma),

[0125] Khuf formation, in Saudi Arabia (basin surface area=250×250 km²,duration of the formation studied=50 Ma),

[0126] The Tortonian and Messinian formations forming the Balearicislands (basin surface area=80×108 km², duration of the formationstudied=6 Ma),

[0127] mixed carbonate systems (sand and clay interacting with coral andrudistid reefs, deep-sea ooze, etc.) in shallow marine environments,

[0128] Miocene formation in Turkey (basin surface area=40×40 km²,duration of the formation studied=5 Ma),

[0129] lower Cretaceous formations, in Oman (basin surface area=100×200km², duration of the formation studied=17 Ma).

[0130] These applications allow showing that the diffusive modelpresented within the scope of the present invention allows obtainingvery precise simulations, with a mean deviation of the cumulativethicknesses of the sediments of the order of 5 meters to 25 kilometersof the constraint wells (for a formation having a mean thickness of theorder of 100 meters), and a difference between the position of thesimulated and observed shores below 10 kilometers (the size of thecalculating grid cells being 10 kilometers).

[0131] As a result of this geometric and faciologic restoration, and ofthe access to the large-scale physics of the sedimentary processes, thediffusive model according to the invention allows going back to thegeologic databases by refining for example the value of the bathymetriesand of the sediment flows, by restoring the accommodation evolution intime and by confirming or invalidating the selection of a correlationscheme.

1-4. (canceled)
 5. A method for forming a diffusive type deterministicmodel for simulating multilithologic filling of a sedimentary basin,comprising: from known field data relative to an architecture of thebasin and measured data or seismic data, forming a set of input datarelative to an accommodation available through subsidence and eustasy,to a supply of fluvial or marine sediments and transportation thereof,and to physical parameters of lithologies, by an iterative processinvolving gridding the basin into grid cells of regular dimensions,modelling according to an explicit finite-volume scheme with constanttime intervals, to simulate flow of each lithology deposited on eachgrid cell; and comparing simulation results with the data and modifyingthe set of input data step by step by inversion; and wherein for eachtime interval and for each lithology modelling by deterministicequations respectively a) a mean of a transportation processes acting ona permanent and continuous basis for a longer term, b) a mean oftransportation processes acting on a permanent and continuous basis fora shorter term, and c) a mean of a transportation processes acting in acatastrophic way for a term less than the shorter term; and determininga resulting stratigraphy of the basin by accounting for the massconservation.
 6. A method as claimed in claim 5, comprising, in eachtime interval and for each lithology: modelling the longer-term flows ofsediments carried by water by accounting for a model of a distributionof water flowing in the basin and of the sediment transportationcapacity of the water flowing in the basin; modelling the shorter-termflows of sediments carried by water using an exponential model forestimating water velocity; and modelling catastrophic flows of sedimentscarried by water in unstable zones located by applying a critical slopecriterion.
 7. A method as claimed in claim 5, wherein in the longer-termflows are modelled by the relation as follows: {right arrow over(Q_(litho))}=λ{right arrow over (Q _(max,litho))}=−λ(K _(gravity) +K_(river) Q _(water)){right arrow over (grad)}z where: Qmax,litho istransportation capacity of the lithology at any point of the basin;Qwater is a water stream flowing at the soil surface at a point;Kgravity is a diffusion coefficient related to permanent gravityprocesses; Kriver is a diffusion coefficient related to permanent riverand ocean transportation; z is an altitude of the soil at a point; and λis a weighting coefficient. 8) A method as claimed in claim 6, whereinin the longer-term flows are modelled by the relation as follows: {rightarrow over (Q_(litho))}=λ{right arrow over (Q _(max,litho))}=λ(K_(gravity) +K _(river) Q _(water)){right arrow over (grad)}z where:Qmax,litho is transportation capacity of the lithology at any point ofthe basin; Qwater is a water stream flowing at the soil surface at apoint; Kgravity is a diffusion coefficient related to permanent gravityprocesses; Kriver is a diffusion coefficient related to permanent riverand ocean transportation; z is an altitude of the soil at a point; and λis a weighting coefficient. 9) A method as claimed in claim 5, whereinthe shorter-term flow of sediment carried by water is modelled byapplying an exponential model for water velocity comprising: U(M)=U_(e)+(U _(o) −U _(e))e ^(ξ/L) ^(_(e)) where Uo represents velocity at areference point of the flow of sediment carried by water, Ue is a waterequilibrium velocity, and ξ is a distance along the flow of sedimentcarried by water, the flows of sediment carried by water being estimatedby a relation:$\overset{\rightarrow}{Q_{\max,{litho}}} = {{- \left( {K_{gravity} + {K_{river}Q_{water}{P(U)}}} \right)}\overset{\rightarrow}{grad}z}$${{with}\quad {P(U)}} = {{\left( \frac{U^{2} - U_{c,{litho}}^{2}}{U_{e}^{2}} \right)^{3/2}\quad {if}\quad U} > U_{c,{litho}}}$and  P(U) = 0  if  U < U_(c, litho)

where P(U) is a weighting coefficient of a velocity model depending on avelocity U of the flow of sediment carried by water, of a criticalvelocity Uc,litho from which each lithology can be transported. 10) Amethod as claimed in claim 6, wherein the shorter-term flow of sedimentcarried by water is modelled by applying an exponential model for watervelocity comprising: U(M)=U _(e)+(U _(o) −U _(e))e ^(−ξ/L) ^(_(e)) whereUo represents velocity at a reference point of the flow of sedimentcarried by water, Ue is a water equilibrium velocity, and ξ is adistance along the flow of sediment carried by water, the flows ofsediment carried by water being estimated by a relation:$\overset{\rightarrow}{Q_{\max,{litho}}} = {{- \left( {K_{gravity} + {K_{river}Q_{water}{P(U)}}} \right)}\overset{\rightarrow}{grad}\quad z\quad {with}}$${P(U)} = {{\left( \frac{U^{2} - U_{c,{litho}}^{2}}{U_{e}^{2}} \right)^{3/2}\quad {if}\quad U} > {U_{c,{litho}}\quad {and}}}$P(U) = 0  if  U > U_(c, litho)

where P(U) is a weighting coefficient of a velocity model depending on avelocity U of the flow of sediment carried by water, of a criticalvelocity Uc,litho from which each lithology can be transported.